A thin Lie algebra is a L, graded over the positive integers, with its first homogeneous component L1 of dimension two and generating such that each nonzero ideal L lies between consecutive terms lower central series. All components have one or two, two-dimensional are called diamonds. If only diamond, then maximal class. We present simpler proofs some fundamental facts on algebras class, algeb...

In the first part of paper, one-parameter (1P), fifth and seventh order polynomial interpolationconvolution kernels, are described. second paper an Experiment is The precision theimage interpolation was tested. Interpolation Test images from base, using wereperformed. kernels measured mean squared error (MSE). Next,optimum kernel parameter, α, were determined by minimizing MSE. After that, a co...

We introduce a new variant MP-LWE of the Learning With Errors problem (LWE) making use of the Middle Product between polynomials modulo an integer q. We exhibit a reduction from the PolynomialLWE problem (PLWE) parametrized by a polynomial f , to MP-LWE which is defined independently of any such f . The reduction only requires f to be monic with constant coefficient coprime with q. It incurs a ...

We introduce the cross-composition framework for proving kernelization lower bounds. A classical problem L and/or-cross-composes into a parameterized problem Q if it is possible to efficiently construct an instance of Q with polynomially bounded parameter value that expresses the logical and or or of a sequence of instances of L. Building on work by Bodlaender et al. (ICALP 2008) and using a re...

In this paper, we present an LMI-based approach for comfort-oriented cruise control of autonomous vehicle. First, vehicle longitudinal dynamics and a corresponding parameter-dependent state-space representation are explained discussed. An polytopic LQR controller is then designed the speed to track reference value in presence noise disturbances, where scheduling parameters functions mass itself...

We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, ux, uxx, uxxx for the Krichever-Novikov equation ut = uxxx−3uxx/(2ux)+p(u)/ux+aux in the case when the polynomial p(u) = 4u − g2u − g3 has distinct roots. We prove that there is a universal prolongation algebra isomorphic to the direct sum of a commutative 2-dimensional algebra and a certain subalgebr...

We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, ux, uxx, uxxx for the Krichever-Novikov equation ut = uxxx−3uxx/(2ux)+p(u)/ux+aux in the case when the polynomial p(u) = 4u − g2u − g3 has distinct roots. We prove that there is a universal prolongation algebra isomorphic to the direct sum of a commutative 2-dimensional algebra and a certain subalgebr...